Couples in engineering mechanics: identify the correct characteristics Which statements about a pure couple (a free vector system of two equal, opposite, parallel forces separated by a distance) are correct?

Introduction / Context:
Couples are fundamental in statics. They represent a pure rotational effect independent of the choice of origin. Recognizing their properties is key for reducing force systems and analyzing beams, frames, mechanisms, and machine elements subjected to torques.

Given Data / Assumptions:

• A couple consists of two equal, opposite, parallel forces separated by a finite arm.
• Rigid body mechanics with classical moment definitions.
• Moments are computed about arbitrary points in the plane/space.

Concept / Approach:

Because net force is zero, a couple does not translate a body but tends to rotate it. Its moment M = F * d is a free vector (in 2D, a scalar with sign) and is invariant about any reference point. Balance of a couple requires an equal and opposite couple; a single force cannot null a free moment since any single force introduces a resultant force not equal to zero.

Step-by-Step Solution:

Verification / Alternative check:

Replacing distributed loads by equivalent resultant and couple shows invariance of the couple part under shift of the line of action, confirming (b).

Why Other Options Are Wrong:

Each individual statement (a)–(d) is correct; therefore the comprehensive correct choice is “All of the above”.

Common Pitfalls:

Confusing a couple with a torque applied via a force at an offset; forgetting that moving a couple anywhere in the body does not change its effect.

Final Answer:

All of the above.